The archive.

Assembled from roughly three hundred pre-war price series across England, Germany, the United States and beyond, this statistical study argues that the trade cycle cannot be read off any single index number. Published in Vienna by Springer with a foreword by Oskar Morgenstern and backing from the Austrian Institute for Trade Cycle Research and the London School of Economics, Tintner applies Anderson's Variate Difference Method and moving averages to decompose each series into trend, cyclical and seasonal components. His finding is that prices move unevenly — metals and interest rates on their own rhythm, textiles and foodstuffs on another — so that the notion of a general price level dissolves. He offers the results not as proof of causes but as ordered material for the theorist, cautiously favouring the monetary cycle theories of Wicksell, Mises and Hayek.

We consider time, on the contrary, only as a kind of auxiliary variable, which we must eliminate in order to bring out the economic relations.

For Gerhard Tintner, reliable confirmation can matter more than striking novelty. His 1936 review of Allen and Bowley’s Family Expenditure praises their use of household budgets to connect demand theory with statistical evidence, while questioning one simplifying assumption: a linear preference scale maintained throughout the investigation. Where that assumption appears to fail, he wants statistical tests, not merely a workable approximation. This brief review offers a concrete view of Tintner’s standards for econometric research: close knowledge of the data, explicit testing of theoretical assumptions, and economic interpretation of numerical results. His praise turns on what the calculations establish about household spending—not on mathematical sophistication alone.

A consumer’s satisfaction may depend not only on how much is consumed, but on whether consumption is increasing or declining. In this 1936 article, Gerhard Tintner asks how that dependence changes the allocation of a fixed income across goods and over time. Familiarity with luxuries and a desire for novelty motivate his mathematical departure from static consumer theory. Using the calculus of variations, he replaces ordinary marginal utility with a valuation corrected for the changing influence of consumption flows. Readers can follow how familiar expenditure rules survive in altered form—and why a budget alone cannot determine a consumption path. Tintner’s explicit distinction between necessary and sufficient conditions also marks the limits of what his equations establish.

What makes a mathematical model economically persuasive rather than merely tractable? In this review of Charles Frederick Roos’s Dynamic Economics, Gerhard Tintner welcomes new ways of analysing time lags and demand while questioning the assumptions that make their calculation possible. Linear demand curves and quadratic costs may be useful approximations, he argues, but conclusions drawn from them need explicit qualification. His sympathy for Roos’s methods sharpens rather than softens his criticism: analyses of particular markets cannot by themselves explain economy-wide employment, expectations, or cyclical fluctuations. The review offers a concrete encounter with the tension between mathematical innovation and economic justification, showing why Tintner values dynamic methods yet asks for stronger theoretical constraints and closer attention to systemic interdependence.

Economic statistics can guide governments and businesses without giving researchers a mandate to make policy. That distinction anchors Gerhard Tintner’s 1936 article on international business-cycle research, written in connection with a congress of research institutes in Vienna. Tintner treats these institutes as necessary responses to economies too complex to understand through personal experience alone, while insisting that their figures remain probabilistic and require economic interpretation. His account brings statistical methods into contact with the Austrian institute’s theoretical commitments, showing why neither data collection nor theory can suffice independently. Readers can discover a concrete conception of research cooperation: shared methods and comparable reports should improve the evidence available for international policy, while independence from state influence and private interests protects the institutes’ capacity to report objectively.

A rising price may prompt buyers to purchase now—or to wait for an expected reversal. In this 1937 article, Gerhard Tintner makes that ambiguity central to monopoly analysis: demand responds not only to the current price but also to its movement over time. His distinctive aim is to connect the mathematical optimization of a price path with familiar economic concepts, especially elasticities, revenues, and marginal costs. Readers can follow how static monopoly conditions change when the seller maximizes profit across an interval rather than at a single moment. Equally revealing is Tintner’s restraint: extending demand to higher price derivatives yields more general equations, but their economic meaning becomes less clear. The article asks how far mathematical generalization can go while remaining economically intelligible.

Economics supplies mathematics with problems, not merely a field for applying established tools: this is the distinctive emphasis of Gerhard Tintner’s 1938 review of R. G. D. Allen’s Mathematical Analysis for Economists. Tintner asks whether mathematics’ close historical association with physics and astronomy has narrowed its attention. Industrial location, monopoly pricing and saving offer concrete alternatives, linking economic questions to geometry, optimization and the calculus of variations. His praise of Allen thus becomes a case for changing what mathematicians study and teachers use as examples. This short review lets readers examine a reciprocal view of mathematical economics: economists acquire analytical methods, while mathematicians encounter problems that may broaden their subject’s customary priorities.

Would it not be interesting for any mathematician to supplement the well known and worn out examples from physics by some economic applications?

Government price fixing poses different problems depending on who competes with whom. In this brief review of Arnold Horwitz’s doctoral thesis, Gerhard Tintner values precisely that comparative approach: minimum prices, maximum prices, and direct price fixation examined across competitive and monopolistic markets. He places Horwitz’s analysis at the intersection of Mises’s work on price regulation and Stackelberg’s account of market organization, while noting its engagement with English and American scholarship. Tintner’s praise also marks a boundary: imperfect competition, selling costs, and price discrimination remain subjects for further investigation. The review offers a compact critical appraisal of what a differentiated theory of price controls should address, rather than an account of the effects of particular controls.

Saving connects today’s purchases with tomorrow’s possibilities—but what does that connection require of a consumer’s valuations? In this compact mathematical article, Gerhard Tintner extends the equalization of marginal utility per unit of expenditure across consumption dates. Expected interest rates link the marginal utilities of money at different times, rather than entering as a separately imposed psychological discount factor. His distinctive approach allows utility to depend on an entire consumption plan, without assuming independent satisfactions at each date, and carries this logic from discrete choices to continuous consumption streams. Readers can discover how successive budgets become a single discounted constraint, and why ratios of marginal utilities carry the relevant economic content. Tintner also marks the limits of his derivation: equilibrium conditions alone do not guarantee a maximum, and empirical verification remains unfinished.

A change in expected interest rates alters not only the value of future income but also the relative cost of consumption at different dates. In this article, Gerhard Tintner extends Hicks and Allen’s demand theory to that intertemporal problem, treating dated commodities as parts of a single consumption plan constrained by a discounted budget. His derivation shows how saving and substitution across dates enter demand’s response to expected incomes, prices, and accumulation rates. The analysis also makes a revealing distinction: demand derived from definite expectations becomes demand expressed through past economic conditions only if the dependence of those expectations on the past is known. Readers can discover both the mathematical structure of this extension of ordinal utility theory and the precise point at which a separate theory of expectations is still needed.

A fall in demand need not mean a fall in spending: the price itself changes the expenditure calculation. In this 1939 article, Gerhard Tintner extends that distinction to consumption planned across time, asking how income, prices, and interest rates alter spending on particular goods and dates. His elasticities separate changes in quantities chosen from the direct effects of prices and discounting. Although total net saving is zero over the planning horizon, borrowing or saving along the way still matters for expenditure responses. The contrast with Irving Fisher sharpens Tintner’s perspective: preferences concern individual goods at particular dates, not merely aggregate expenditure streams. Readers can discover how aggregation preserves these distinctions—and why quantity-demand elasticities alone cannot explain changes in spending.

What mathematics should economists learn, and how should it be taught? In this 1939 review of R. G. D. Allen’s Mathematical Analysis for Economists, Gerhard Tintner values economic applications over the physical examples customary in calculus textbooks. Constrained optimization is his telling case: a technique central to economics receives the sustained attention economists need. His praise also draws a useful distinction between teaching mathematical tools through consumer choice, monopoly, and production, and presenting a continuous economic theory. Yet the book’s predominantly static approach leaves dynamic problems underrepresented. This brief review offers a concrete view of Tintner’s standards for graduate training: mathematical instruction should prepare economists to follow current research, while its omissions should guide their supplementary study.